First, on balanced versus unbalanced. Whenever this option comes up, you really have to try it to see if one is better than the other with your components.
For instance I have Audio Research equipment. ARC recommends the use of balanced interconnects because the internal designs of both the amp and preamp are balanced. I tried both, I can’t tell the difference. This is not always true, but typically it is not a big difference if any difference can be heard (other than volume…. Which is of no consequence to your system… it will not play louder, it is just the characteristic of the interconnects). My point is, this is not a reason to swap amps… particularly to one older than ten years. It is more likely… the difference in character or age will have a bigger impact.
But if you want a new amp… great idea… focus on the amp / sound character and as you are getting close… just verify it is a balanced design. I would put this at the very end of the list of requirements.